A screening machine of this type is known from German Pat. No. 1,206,372. Reference may also be had to U.S. Pat. Nos. 3,971,715 and 4,600,506 in the regard. The mutually opposite side members of the two systems of movement have two driven eccentric shafts passing through them. The two ends of each shaft are mounted rotatably in a base frame. This additional base frame involves a high outlay in construction cost and means that the machine must be of a large overall size. Furthermore, considerable vibrational force must be absorbed by this base frame.